From The Collaborative International Dictionary of English v.0.48:

Border \Bor"der\, v. i. [imp. & p. p. Bordered; p. pr. & vb.
   n. Bordering.]
   1. To touch at the edge or boundary; to be contiguous or
      adjacent; -- with on or upon as, Connecticut borders on
      Massachusetts.
      [1913 Webster]

   2. To approach; to come near to; to verge.
      [1913 Webster]

            Wit which borders upon profaneness deserves to be
            branded as folly.                     --Abp.
                                                  Tillotson.
      [1913 Webster]

From Moby Thesaurus II by Grady Ward, 1.0:

58 Moby Thesaurus words for "bordering":
   adjacent, adjoining, beading, binding, borderline, bordure,
   boundary, bounding, coastal, connecting, conterminous, contiguous,
   coterminous, determinant, determinative, determining, edging,
   end to end, endways, endwise, extreme, face to face, fimbria,
   fimbriation, flounce, frill, frilling, fringe, fringing, frontier,
   furbelow, galloon, hem, immediate, joined, juxtaposed,
   juxtapositional, juxtapositive, limbic, liminal, limit, limiting,
   list, littoral, marginal, motif, neighbor, neighboring, next,
   rimming, ruffle, selvage, skirting, terminal, threshold, trimming,
   valance, welt